Problem: $\dfrac{ 7j + 10k }{ 4 } = \dfrac{ -9j - 3l }{ 8 }$ Solve for $j$.
Solution: Multiply both sides by the left denominator. $\dfrac{ 7j + 10k }{ {4} } = \dfrac{ -9j - 3l }{ 8 }$ ${4} \cdot \dfrac{ 7j + 10k }{ {4} } = {4} \cdot \dfrac{ -9j - 3l }{ 8 }$ $7j + 10k = {4} \cdot \dfrac { -9j - 3l }{ 8 }$ Multiply both sides by the right denominator. $7j + 10k = 4 \cdot \dfrac{ -9j - 3l }{ {8} }$ ${8} \cdot \left( 7j + 10k \right) = {8} \cdot 4 \cdot \dfrac{ -9j - 3l }{ {8} }$ ${8} \cdot \left( 7j + 10k \right) = 4 \cdot \left( -9j - 3l \right)$ Distribute both sides ${8} \cdot \left( 7j + 10k \right) = {4} \cdot \left( -9j - 3l \right)$ ${56}j + {80}k = -{36}j - {12}l$ Combine $j$ terms on the left. ${56j} + 80k = -{36j} - 12l$ ${92j} + 80k = -12l$ Move the $k$ term to the right. $92j + {80k} = -12l$ $92j = -12l - {80k}$ Isolate $j$ by dividing both sides by its coefficient. ${92}j = -12l - 80k$ $j = \dfrac{ -12l - 80k }{ {92} }$ All of these terms are divisible by $4$ $j = \dfrac{ -{3}l - {20}k }{ {23} }$